Abstract and Applied Analysis
Volume 2003 (2003), Issue 7, Pages 435-448

Birkhoff-Kellogg theorems on invariant directions for multimaps

Ravi P. Agarwal1 and Donal O'Regan2

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland

Received 11 December 2001

Copyright © 2003 Ravi P. Agarwal and Donal O'Regan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and 𝒰cκ maps.